A wave is essentially a disturbance that travels through a medium. As a wave travels, it shifts the particles in the medium (solid, liquid or gas) from their resting equilibrium positions. Earthquakes occur when a disturbance (a break or shift in tectonic plates) travels through the solid rock of the earth. Tsunamis occur when the disturbance caused by an earthquake travels through the ocean, causing a really big ocean wave (get it?) Sound from your television's speakers travel as sound waves (disturbances of the air particles) towards your ears. Your microwave heats up food by producing electromagnetic radiation in the (you guessed it) microwave frequency range to cause molecules in the food to rotate and produce heat in dielectric heating. These occurrences all happen due to the creation and propagation of waves.
There are two fundamental types of waves: longitudinal waves and transverse waves. The difference between them is in how they travel.
Longitudinal waves shift the particles in the medium they travel through in a direction parallel to the movement of the wave itself. A longitudinal wave is made up of two cycles, compressions (particles are squeezed together) and rarefactions (particles are spread out).
As you can see in the graphic above, the particles are being compressed and then spread out again in the direction of the motion of the wave.
By contrast, transverse waves shift particles in a direction perpendicular to the movement of the wave. So, it transfers energy perpendicular to the direction of its propagation.
Above, you can see a transverse wave that sort of resembles what happens whenever you grab one end of a rope and wave it up and down. The wave travels down the rope and motion that resembles the graphic above is the result. The dotted line represents the direction of the movement of the wave and the undulating line represents the movement of the particles in relation to the wave.
These two types of waves can either be pulses or progressive waves. A pulse is a sudden disturbance where only one wave or a few waves are generated, such as when a pebble is dropped into a puddle. A few waves are visible in the water but they eventually disappear. Thunder and explosions also create pulses. A progressive wave repeats the same oscillation for several cycles, and is associated with simple harmonic motion. Each particle in the medium experiences simple harmonic motion in periodic waves by moving back and forth repetitively through the same positions. (Note: Simple harmonic motion is repetitive motion where the object moves back and forth through an equilibrium or central position so maximum displacement on one side of the central position is equal to maximum displacement on the other side)
We already covered the fact that a wave displaces particles from their equilibrium/resting positions. When this is represented on a graph of displacement-position like the one above, we can see both the negative and positive displacement from the original position. Wavelength (λ) is essentially the distance between two successive crests of the wave, or the distance between another two corresponding points on the wave. Amplitude (A) is the height of the wave, or the distance between the equilibrium position and the highest point (crest) of the wave. It can also be defined as the maximum displacement from the equilibrium position. (Note: a progressive wave varies in both time and space/position simultaneously. To represent it on paper, either time or position must be held constant. In the graph above, time would be constant.)
As an additional side note, displacement on the graph above represents displacement of the wave, or any point in relation to the wave.
Now, if we represent the wave graphically keeping position constant, we get a displacement-time graph.
The time between two crests of the wave (or two corresponding points on the wave) is known as the period (T) of the wave.
CSEC also requires that you understand the concept of the frequency of a wave. The frequency (f) of a wave is how frequently it completes one cycle or oscillation in a given time period. It is related to the period (T) of a wave like this:
f = 1/T
f = T⁻¹
Frequency is measured in Hertz (hz), or seconds per cycle.
As you might have already guessed, wave speed (v) is how quickly a wave travels. This can be calculated like this:
v = f × λ
v = λ/T